Calculate Nth root with integer arithmetic

Question

There are a couple of ways to find integer square roots using only integer arithmetic. For example this one. It makes for interesting reading and also a very interesting the

Answer 1

It seems to me that the Shifting nth root algorithm provides exactly what you want:

The shifting nth root algorithm is an algorithm for extracting the nth root of a positive real number which proceeds iteratively by shifting in n digits of the radicand, starting with the most significant, and produces one digit of the root on each iteration, in a manner similar to long division.

There are worked examples on the linked wikipedia page.